text:
<!DOCTYPE html>

  <meta charset="utf-8">

  <meta name="viewport" content="width=device-width, initial-scale=1.0">

  <title>pydrake.systems.controllers — pydrake  documentation</title>

  <link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
  <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
  <link rel="stylesheet" href="_static/css/custom.css" type="text/css" />
    <link rel="index" title="Index" href="genindex.html" />
    <link rel="search" title="Search" href="search.html" />
    <link rel="next" title="pydrake.systems.drawing" href="pydrake.systems.drawing.html" />
    <link rel="prev" title="pydrake.systems.analysis" href="pydrake.systems.analysis.html" />

          Home

          Installation

          Gallery

API Documentation

            C++ Python

Resources

            Getting Help Tutorials Python Bindings For Developers Credits

          GitHub

             pydrake

  <form id="rtd-search-form" class="wy-form" action="search.html" method="get">
    <input type="text" name="q" placeholder="Search pydrake only…" />
    <input type="hidden" name="check_keywords" value="yes" />
    <input type="hidden" name="area" value="default" />
  </form>
  <form id="ddg-search-form" class="wy_form" action="https://duckduckgo.com/" method="get">
    <input type="text" name="q" placeholder="Search all of Drake…" />
    <input type="hidden" name="sites" value="drake.mit.edu" />
  </form>

pydrake.all

pydrake.autodiffutils

pydrake.common

pydrake.examples

pydrake.forwarddiff

pydrake.geometry

pydrake.lcm

pydrake.manipulation

pydrake.math

pydrake.multibody

pydrake.perception

pydrake.polynomial

pydrake.solvers

pydrake.symbolic

pydrake.systems

pydrake.systems.all

pydrake.systems.analysis

pydrake.systems.controllers

pydrake.systems.drawing

pydrake.systems.framework

pydrake.systems.lcm

pydrake.systems.perception

pydrake.systems.planar_scenegraph_visualizer

pydrake.systems.primitives

pydrake.systems.pyplot_visualizer

pydrake.systems.rendering

pydrake.systems.scalar_conversion

pydrake.systems.sensors

pydrake.systems.trajectory_optimization

pydrake.trajectories

pydrake.tutorials

pydrake.visualization

          pydrake

Docs »

pydrake.systems »

pydrake.systems.controllers

pydrake.systems.controllers¶

pydrake.systems.controllers.DiscreteTimeLinearQuadraticRegulator(A: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], B: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], Q: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], R: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous]) → Tuple[numpy.ndarray[numpy.float64[m, n]], numpy.ndarray[numpy.float64[m, n]]]¶

Computes the optimal feedback controller, u=-Kx, and the optimal
cost-to-go J = x'Sx for the problem:

\[x[n+1] = Ax[n] + Bu[n]\]

\[\min_u \sum_0^\infty x'Qx + u'Ru\]

Parameter A:

The state-space dynamics matrix of size num_states x num_states.

Parameter B:

The state-space input matrix of size num_states x num_inputs.

Parameter Q:

A symmetric positive semi-definite cost matrix of size num_states
x num_states.

Parameter R:

A symmetric positive definite cost matrix of size num_inputs x
num_inputs.

<col class="field-name" />
<col class="field-body" />

Returns:	A structure that contains the optimal feedback gain K and the
quadratic cost term S. The optimal feedback control is u = -Kx;

Raises:	RuntimeError if R is not positive definite.

class pydrake.systems.controllers.DynamicProgrammingOptions¶

Consolidates the many possible options to be passed to the dynamic
programming algorithms.

__init__(self: pydrake.systems.controllers.DynamicProgrammingOptions) → None¶

assume_non_continuous_states_are_fixed¶

(Advanced) Boolean which, if true, allows this algorithm to optimize
without considering the dynamics of any non-continuous states. This is
helpful for optimizing systems that might have some additional
book-keeping variables in their state. Only use this if you are sure
that the dynamics of the additional state variables cannot impact the
dynamics of the continuous states. $*Default:* false.

convergence_tol¶

Value iteration methods converge when the value function stops
changing (typically evaluated with the l∞ norm). This value sets that
threshold.

discount_factor¶

A value between (0,1] that discounts future rewards.

See also

FittedValueIteration.

input_port_index¶

For systems with multiple input ports, we must specify which input
port is being used in the control design.

See also

systems::InputPortSelection.

periodic_boundary_conditions¶

class PeriodicBoundaryCondition¶

For algorithms that rely on approximations of the state-dynamics (as
in FittedValueIteration), this is a list of state dimensions for which
the state space maximum value should be "wrapped around" to ensure
that all values are in the range [low, high). The classic example is
for angles that are wrapped around at 2π.

__init__(self: pydrake.systems.controllers.DynamicProgrammingOptions.PeriodicBoundaryCondition, state_index: int, low: float, high: float) → None¶

high¶

low¶

state_index¶

visualization_callback¶

If callable, this method is invoked during each major iteration of the
dynamic programming algorithm, in order to facilitate e.g. graphical
inspection/debugging of the results.

Note

The first call happens at iteration 1 (after the value iteration
has run once), not zero.

pydrake.systems.controllers.FiniteHorizonLinearQuadraticRegulator(system: pydrake.systems.framework.System_[float], context: pydrake.systems.framework.Context_[float], t0: float, tf: float, Q: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], R: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], options: pydrake.systems.controllers.FiniteHorizonLinearQuadraticRegulatorOptions = FiniteHorizonLinearQuadraticRegulatorOptions(Qf=None, N=None, input_port_index=InputPortSelection.kUseFirstInputIfItExists, use_square_root_method=False)) → pydrake.systems.controllers.FiniteHorizonLinearQuadraticRegulatorResult¶

Solves the differential Riccati equation to compute the optimal
controller and optimal cost-to-go for the finite-horizon linear
quadratic regulator:

\[\min_u (x(t_f)-x_d(t_f))'Q_f(x(t_f)-x_d(t_f)) + \int_{t_0}^{t_f}\]

(x(t)-x_d(t))'Q(x(t)-x_d(t)) dt + int_{t_0}^{t_f}
(u(t)-u_d(t))'R(u(t)-u_d(t)) dt + int_{t_0}^{t_f}
2(x(t)-x_d(t))'N(u(t)-u_d(t)) dt text{s.t. } dot{x} - dot{x}_0(t) = A(t)(x(t) - x_0(t)) + B(t)(u(t) -
u_0(t)) + c(t)

where A(t), B(t), and c(t) are taken from the gradients of the
continuous-time dynamics ẋ = f(t,x,u), as A(t) = dfdx(t, x0(t),
u0(t)), B(t) = dfdu(t, x0(t), u0(t)), and c(t) = f(t, x0(t), u0(t)) -
ẋ0(t). x0(t) and u0(t) can be specified in options, otherwise are
taken to be constant trajectories with values given by context.

Parameter system:

a System<double> representing the plant.

Parameter context:

a Context<double> used to pass the default input, state, and
parameters. Note: Use options to specify time-varying nominal
state and/or input trajectories.

Parameter t0:

is the initial time.

Parameter tf:

is the final time (with tf > t0).

Parameter Q:

is nxn positive semi-definite.

Parameter R:

is mxm positive definite.

Parameter options:

is the optional FiniteHorizonLinearQuadraticRegulatorOptions.

Precondition:

system must be a System<double> with (only) n continuous state
variables and m inputs. It must be convertable to
System<AutoDiffXd>.

Note

Support for difference-equation systems (

See also

System<T>::IsDifferenceEquationSystem()) by solving the
differential Riccati equation and richer specification of the
objective are anticipated (they are listed in the code as TODOs).

class pydrake.systems.controllers.FiniteHorizonLinearQuadraticRegulatorOptions¶

A structure to facilitate passing the myriad of optional arguments to
the FiniteHorizonLinearQuadraticRegulator algorithms.

__init__(self: pydrake.systems.controllers.FiniteHorizonLinearQuadraticRegulatorOptions) → None¶

input_port_index¶

For systems with multiple input ports, we must specify which input
port is being used in the control design.

See also

systems::InputPortSelection.

N¶

A num_states x num_inputs matrix that describes the running cost
2(x-xd(t))'N(u-ud(t)). If unset, then N will be set to the zero
matrix.

Qf¶

A num_states x num_states positive semi-definite matrix which
specified the cost at the final time. If unset, then Qf will be set to
the zero matrix.

u0¶

A nominal input trajectory. The system is linearized about this
trajectory. u0 must be defined over the entire interval, [t0, tf]. If
null, then u0 is taken to be a constant trajectory (whose value is
specified by the context passed into the LQR method).

ud¶

A desired input trajectory. The objective is to regulate to this
trajectory – the input component of the quadratic running cost is
(u-ud(t))'*R*(u-ud(t)). If null, then ud(t) = u0(t).

use_square_root_method¶

Enables the "square-root" method solution to the Riccati equation.
This is slightly more expensive and potentially less numerically
accurate (errors are bounded on the square root), but is more
numerically robust. When True, then you must also set a (positive
definite and symmetric) Qf in this options struct.

x0¶

A nominal state trajectory. The system is linearized about this
trajectory. x0 must be defined over the entire interval [t0, tf]. If
null, then x0 is taken to be a constant trajectory (whose value is
specified by the context passed into the LQR method).

xd¶

A desired state trajectory. The objective is to regulate to this
trajectory – the state component of the quadratic running cost is
(x-xd(t))'*Q*(x-xd(t)) and the final cost is (x-xd(t))'Qf(x-xd(t)). If
null, then xd(t) = x0(t).

class pydrake.systems.controllers.FiniteHorizonLinearQuadraticRegulatorResult¶

A structure that contains the basic
FiniteHorizonLinearQuadraticRegulator results. The finite-horizon
cost-to-go is given by (x-x0(t))'*S(t)*(x-x0(t)) + 2*(x-x₀(t))'sₓ(t) +
s₀(t) and the optimal controller is given by u-u0(t) = -K(t)*(x-x₀(t))
- k₀(t). Please don't overlook the factor of 2 in front of the sₓ(t)
term.

__init__¶

Initialize self.  See help(type(self)) for accurate signature.

K¶

This K is the K_x term in the derivation notes.

<col class="field-name" />
<col class="field-body" />

Type:	Note

k0¶

S¶

s0¶

sx¶

u0¶

x0¶

pydrake.systems.controllers.FittedValueIteration(arg0: pydrake.systems.analysis.Simulator_[float], arg1: Callable[[pydrake.systems.framework.Context_[float]], float], arg2: List[Set[float]], arg3: List[Set[float]], arg4: float, arg5: pydrake.systems.controllers.DynamicProgrammingOptions) → Tuple[pydrake.systems.primitives.BarycentricMeshSystem, numpy.ndarray[numpy.float64[1, n]]]¶

Implements Fitted Value Iteration on a (triangulated) Barycentric
Mesh, which designs a state-feedback policy to minimize the
infinite-horizon cost ∑ γⁿ g(x[n],u[n]), where γ is the discount
factor in options.

For background, and a description of this algorithm, see
http://underactuated.csail.mit.edu/underactuated.html?chapter=dp . It
currently requires that the system to be optimized has only continuous
state and it is assumed to be time invariant. This code makes a
discrete-time approximation (using timestep) for the value
iteration update.

Parameter simulator:

contains the reference to the System being optimized and to a
Context for that system, which may contain non-default Parameters,
etc. The simulator is run for timestep seconds from every
point on the mesh in order to approximate the dynamics; all of the
simulation parameters (integrator, etc) are relevant during that
evaluation.

Parameter cost_function:

is the continuous-time instantaneous cost. This implementation of
the discrete-time formulation above uses the approximation g(x,u)
= timestep*cost_function(x,u).

Parameter state_grid:

defines the mesh on the state space used to represent the
cost-to-go function and the resulting policy.

Parameter input_grid:

defines the discrete action space used in the value iteration
update.

Parameter timestep:

a time in seconds used for the discrete-time approximation.

Parameter options:

optional DynamicProgrammingOptions structure.

<col class="field-name" />
<col class="field-body" />

Returns:	a std::pair containing the resulting policy, implemented as a
BarycentricMeshSystem, and the RowVectorXd J that defines the
expected cost-to-go on a BarycentricMesh using state_grid. The
policy has a single vector input (which is the continuous state of
the system passed in through simulator) and a single vector
output (which is the input of the system passed in through
simulator).

class pydrake.systems.controllers.InverseDynamics¶

Bases: pydrake.systems.framework.LeafSystem_[float]

Solves inverse dynamics with no consideration for joint actuator force
limits.

Computes the generalized force τ_id that needs to be applied so
that the multibody system undergoes a desired acceleration vd_d.
That is, τ_id is the result of an inverse dynamics computation
according to:

τ_id = M(q)vd_d + C(q, v)v - τ_g(q) - τ_app

where M(q) is the mass matrix, C(q, v)v is the bias term
containing Coriolis and gyroscopic effects, τ_g(q) is the vector
of generalized forces due to gravity and τ_app contains applied
forces from force elements added to the multibody model (this can
include damping, springs, etc. See
MultibodyPlant::CalcForceElementsContribution()).

The system also provides a pure gravity compensation mode via an
option in the constructor. In this case, the output is simply

τ_id = -τ_g(q).

InverseDynamicsController uses a PID controller to generate desired
acceleration and uses this class to compute generalized forces. Use
this class directly if desired acceleration is computed differently.

u0 (estimated state)→

u1 (desired accelerations)→

	InverseDynamics

→ y0 (force)

Port u0 accepts system estimated state; port y0 emits
generalized forces. Port u1 is only present when the mode at
construction is not kGravityCompensation. When present, u1
accepts desired accelerations.

__init__(self: pydrake.systems.controllers.InverseDynamics, plant: pydrake.multibody.plant.MultibodyPlant_[float], mode: pydrake.systems.controllers.InverseDynamics.InverseDynamicsMode = <InverseDynamicsMode.kInverseDynamics: 0>) → None¶

Constructs the InverseDynamics system.

Parameter plant:

Pointer to the multibody plant model. The life span of plant
must be longer than that of this instance.

Parameter mode:

If set to kGravityCompensation, this instance will only consider
the gravity term. It also will NOT have the desired acceleration
input port.

Precondition:

The plant must be finalized (i.e., plant.is_finalized() must
return True).

class InverseDynamicsMode¶

Members:

kInverseDynamics :

kGravityCompensation : Purely gravity compensation mode.

__init__(self: pydrake.systems.controllers.InverseDynamics.InverseDynamicsMode, value: int) → None¶

kGravityCompensation = <InverseDynamicsMode.kGravityCompensation: 1>¶

kInverseDynamics = <InverseDynamicsMode.kInverseDynamics: 0>¶

name¶

value¶

is_pure_gravity_compensation(self: pydrake.systems.controllers.InverseDynamics) → bool¶

kGravityCompensation = <InverseDynamicsMode.kGravityCompensation: 1>¶

kInverseDynamics = <InverseDynamicsMode.kInverseDynamics: 0>¶

class pydrake.systems.controllers.InverseDynamicsController¶

Bases: pydrake.systems.framework.Diagram_[float]

A state feedback controller that uses a PidController to generate
desired accelerations, which are then converted into torques using
InverseDynamics. More specifically, the output of this controller is:

force = inverse_dynamics(q, v, vd_command), where
  vd_command = kp(q_d - q) + kd(v_d - v) + ki int(q_d - q) + vd_d.

Here q and v stand for the generalized position and velocity,
and vd is the generalized acceleration. The subscript _d
indicates desired values, and vd_command indicates the
acceleration command (which includes the stabilization terms) passed
to the inverse dynamics computation.

estimated_state→

desired_state→

desired_acceleration→

	InverseDynamicsController

→ force

The desired acceleration port shown in <span
style="color:gray">gray</span> may be absent, depending on the
arguments passed to the constructor.

Note that this class assumes the robot is fully actuated, its position
and velocity have the same dimension, and it does not have a floating
base. If violated, the program will abort. This controller was not
designed for closed-loop systems: the controller accounts for neither
constraint forces nor actuator forces applied at loop constraints. Use
on such systems is not recommended.

See also

InverseDynamics for an accounting of all forces incorporated into
the inverse dynamics computation.

__init__(self: pydrake.systems.controllers.InverseDynamicsController, robot: pydrake.multibody.plant.MultibodyPlant_[float], kp: numpy.ndarray[numpy.float64[m, 1]], ki: numpy.ndarray[numpy.float64[m, 1]], kd: numpy.ndarray[numpy.float64[m, 1]], has_reference_acceleration: bool) → None¶

Constructs an inverse dynamics controller for the given plant
model. The InverseDynamicsController holds an internal, non-owned
reference to the MultibodyPlant object so you must ensure that
plant has a longer lifetime than this
InverseDynamicsController.

Parameter plant:

The model of the plant for control.

Parameter kp:

Position gain.

Parameter ki:

Integral gain.

Parameter kd:

Velocity gain.

Parameter has_reference_acceleration:

If true, there is an extra BasicVector input port for vd_d. If
false, vd_d is treated as zero, and no extra input port is
declared.

Precondition:

plant has been finalized (plant.is_finalized() returns
True).

<col class="field-name" />
<col class="field-body" />

Raises:

RuntimeError if - The plant is not finalized (see

MultibodyPlant::Finalize()). - The number of generalized

velocities is not equal to the number of generalized positions. -

The model is not fully actuated. - Vector kp, ki and kd do not all

have the same size equal to the number of generalized positions.

get_input_port_desired_acceleration(self: pydrake.systems.controllers.InverseDynamicsController) → pydrake.systems.framework.InputPort_[float]¶

Returns the input port for the reference acceleration.

get_input_port_desired_state(self: pydrake.systems.controllers.InverseDynamicsController) → pydrake.systems.framework.InputPort_[float]¶

Returns the input port for the desired state.

get_input_port_estimated_state(self: pydrake.systems.controllers.InverseDynamicsController) → pydrake.systems.framework.InputPort_[float]¶

Returns the input port for the estimated state.

get_multibody_plant_for_control(self: pydrake.systems.controllers.InverseDynamicsController) → pydrake.multibody.plant.MultibodyPlant_[float]¶

Returns a constant pointer to the MultibodyPlant used for control.

get_output_port_control(self: pydrake.systems.controllers.InverseDynamicsController) → pydrake.systems.framework.OutputPort_[float]¶

Returns the output port for computed control.

set_integral_value(self: pydrake.systems.controllers.InverseDynamicsController, arg0: pydrake.systems.framework.Context_[float], arg1: numpy.ndarray[numpy.float64[m, 1]]) → None¶

Sets the integral part of the PidController to value. value
must be a column vector of the appropriate size.

class pydrake.systems.controllers.JointStiffnessController¶

Bases: pydrake.systems.framework.LeafSystem_[float]

Implements a joint-space stiffness controller of the form

τ_control = −τ_g(q) − τ_app + kp⊙(q_d − q) + kd⊙(v_d − v)

where Kp and Kd are the joint stiffness and damping
coefficients, respectively, τ_g(q) is the vector of generalized
forces due to gravity, and τ_app contains applied forces from
force elements added to the multibody model (this can include damping,
springs, etc. See MultibodyPlant::CalcForceElementsContribution()).
q_d and v_d are the desired (setpoint) values for the
multibody positions and velocities, respectively. kd and kp
are taken as vectors, and ⊙ represents elementwise multiplication.

The goal of this controller is to produce a closed-loop dynamics that
resembles a spring-damper dynamics at the joints around the setpoint:

M(q)v̇ + C(q,v)v + kp⊙(q - q_d) + kd⊙(v - v_d) = τ_ext,

where M(q)v̇ + C(q,v)v are the original multibody mass and
Coriolis terms, and τ_ext are any external generalized forces that
can arise, e.g. from contact forces.

The controller currently requires that plant.num_positions() ==
plant.num_velocities() == plant.num_actuated_dofs().

estimated_state→

desired_state→

	JointStiffnessController

→ generalized_force

Note that the joint impedance control as implemented on Kuka's iiwa
and Franka' Panda is best modeled as a stiffness controller (unless
one were to model the actual elastic joints and rotor-inertia
shaping). See https://manipulation.csail.mit.edu/force.html for more
details.

__init__(self: pydrake.systems.controllers.JointStiffnessController, plant: pydrake.multibody.plant.MultibodyPlant_[float], kp: numpy.ndarray[numpy.float64[m, 1]], kd: numpy.ndarray[numpy.float64[m, 1]]) → None¶

Constructs the JointStiffnessController system.

Parameter plant:

Reference to the multibody plant model. The life span of plant
must be at least as long as that of this instance.

Precondition:

The plant must be finalized (i.e., plant.is_finalized() must
return True).

Precondition:

plant.num_positions() == plant.num_velocities() ==
plant.num_actuated_dofs() == kp.size() == kd.size()

get_input_port_desired_state(self: pydrake.systems.controllers.JointStiffnessController) → pydrake.systems.framework.InputPort_[float]¶

Returns the input port for the desired state.

get_input_port_estimated_state(self: pydrake.systems.controllers.JointStiffnessController) → pydrake.systems.framework.InputPort_[float]¶

Returns the input port for the estimated state.

get_multibody_plant(self: pydrake.systems.controllers.JointStiffnessController) → pydrake.multibody.plant.MultibodyPlant_[float]¶

Returns a constant pointer to the MultibodyPlant used for control.

get_output_port_generalized_force(self: pydrake.systems.controllers.JointStiffnessController) → pydrake.systems.framework.OutputPort_[float]¶

Returns the output port for the generalized forces implementing the
control.

pydrake.systems.controllers.LinearProgrammingApproximateDynamicProgramming(arg0: pydrake.systems.analysis.Simulator_[float], arg1: Callable[[pydrake.systems.framework.Context_[float]], float], arg2: Callable[[numpy.ndarray[numpy.float64[m, 1]], numpy.ndarray[object[m, 1]]], pydrake.symbolic.Expression], arg3: int, arg4: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], arg5: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], arg6: float, arg7: pydrake.systems.controllers.DynamicProgrammingOptions) → numpy.ndarray[numpy.float64[m, 1]]¶

Implements the Linear Programming approach to approximate dynamic
programming. It optimizes the linear program

maximize ∑ Jₚ(x). subject to ∀x, ∀u, Jₚ(x) ≤ g(x,u) + γJₚ(f(x,u)),

where g(x,u) is the one-step cost, Jₚ(x) is a (linearly) parameterized
cost-to-go function with parameter vector p, and γ is the discount
factor in options.

For background, and a description of this algorithm, see
http://underactuated.csail.mit.edu/underactuated.html?chapter=dp . It
currently requires that the system to be optimized has only continuous
state and it is assumed to be time invariant. This code makes a
discrete-time approximation (using timestep) for the value
iteration update.

Parameter simulator:

contains the reference to the System being optimized and to a
Context for that system, which may contain non-default Parameters,
etc. The simulator is run for timestep seconds from every
pair of input/state sample points in order to approximate the
dynamics; all of the simulation parameters (integrator, etc) are
relevant during that evaluation.

Parameter cost_function:

is the continuous-time instantaneous cost. This implementation of
the discrete-time formulation above uses the approximation g(x,u)
= timestep*cost_function(x,u).

Parameter linearly_parameterized_cost_to_go_function:

must define a function to approximate the cost-to-go, which takes
the state vector as the first input and the parameter vector as
the second input. This can be any function of the form Jₚ(x) = ∑
pᵢ φᵢ(x). This algorithm will pass in a VectorX of
symbolic::Variable in order to set up the linear program.

Parameter state_samples:

is a list of sample states (one per column) at which to apply the
optimization constraints and the objective.

Parameter input_samples:

is a list of inputs (one per column) which are evaluated at every
sample point.

Parameter timestep:

a time in seconds used for the discrete-time approximation.

Parameter options:

optional DynamicProgrammingOptions structure.

<col class="field-name" />
<col class="field-body" />

Returns:	params the VectorXd of parameters that optimizes the supplied
cost-to-go function.

pydrake.systems.controllers.LinearQuadraticRegulator(*args, **kwargs)¶

Overloaded function.

LinearQuadraticRegulator(A: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], B: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], Q: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], R: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], N: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous] = array([], shape=(0, 0), dtype=float64), F: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous] = array([], shape=(0, 0), dtype=float64)) -> Tuple[numpy.ndarray[numpy.float64[m, n]], numpy.ndarray[numpy.float64[m, n]]]

Computes the optimal feedback controller, u=-Kx, and the optimal
cost-to-go J = x'Sx for the problem:

\[\min_u \int_0^\infty x'Qx + u'Ru + 2x'Nu dt\]

\[\dot{x} = Ax + Bu\]

\[Fx = 0\]

Parameter A:

The state-space dynamics matrix of size num_states x num_states.

Parameter B:

The state-space input matrix of size num_states x num_inputs.

Parameter Q:

A symmetric positive semi-definite cost matrix of size num_states
x num_states.

Parameter R:

A symmetric positive definite cost matrix of size num_inputs x
num_inputs.

Parameter N:

A cost matrix of size num_states x num_inputs. If N.rows() == 0, N
will be treated as a num_states x num_inputs zero matrix.

Parameter F:

A constraint matrix of size num_constraints x num_states. rank(F)
must be < num_states. If F.rows() == 0, F will be treated as a 0 x
num_states zero matrix.

<col class="field-name" />
<col class="field-body" />

Returns:	A structure that contains the optimal feedback gain K and the
quadratic cost term S. The optimal feedback control is u = -Kx;

Raises:	RuntimeError if R is not positive definite.

LinearQuadraticRegulator(system: pydrake.systems.primitives.LinearSystem_[float], Q: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], R: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], N: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous] = array([], shape=(0, 0), dtype=float64)) -> pydrake.systems.primitives.LinearSystem_[float]

Creates a system that implements the optimal time-invariant linear
quadratic regulator (LQR). If system is a continuous-time system,
then solves the continuous-time LQR problem:

\[\min_u \int_0^\infty x^T(t)Qx(t) + u^T(t)Ru(t) + + 2x^T(t)Nu(t) dt.\]

If system is a discrete-time system, then solves the discrete-time
LQR problem:

\[\min_u \sum_0^\infty x^T[n]Qx[n] + u^T[n]Ru[n] + 2x^T[n]Nu[n].\]

Parameter system:

The System to be controlled.

Parameter Q:

A symmetric positive semi-definite cost matrix of size num_states
x num_states.

Parameter R:

A symmetric positive definite cost matrix of size num_inputs x
num_inputs.

Parameter N:

A cost matrix of size num_states x num_inputs.

<col class="field-name" />
<col class="field-body" />

Returns:	A system implementing the optimal controller in the original
system coordinates.

Raises:	RuntimeError if R is not positive definite.

LinearQuadraticRegulator(system: pydrake.systems.framework.System_[float], context: pydrake.systems.framework.Context_[float], Q: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], R: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], N: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous] = array([], shape=(0, 0), dtype=float64), input_port_index: int = 0) -> pydrake.systems.primitives.AffineSystem_[float]

Linearizes the System around the specified Context, computes the
optimal time-invariant linear quadratic regulator (LQR), and returns a
System which implements that regulator in the original System's
coordinates. If system is a continuous-time system, then solves
the continuous-time LQR problem:

\[\min_u \int_0^\infty (x-x_0)^TQ(x-x_0) + (u-u_0)^TR(u-u_0) + 2
(x-x_0)^TN(u-u_0) dt.\]

If system is a discrete-time system, then solves the discrete-time
LQR problem:

\[\min_u \sum_0^\infty (x-x_0)^TQ(x-x_0) + (u-u_0)^TR(u-u_0) +
2(x-x_0)^TN(u-u_0),\]

where \(x_0\) is the nominal state and \(u_0\) is the nominal
input. The system is considered discrete if it has a single discrete
state vector and a single unique periodic update event declared.

Parameter system:

The System to be controlled.

Parameter context:

Defines the desired state and control input to regulate the system
to. Note that this state/input must be an equilibrium point of the
system. See drake::systems::Linearize for more details.

Parameter Q:

A symmetric positive semi-definite cost matrix of size num_states
x num_states.

Parameter R:

A symmetric positive definite cost matrix of size num_inputs x
num_inputs.

Parameter N:

A cost matrix of size num_states x num_inputs. If the matrix is
zero-sized, N will be treated as a num_states x num_inputs zero
matrix.

Parameter input_port_index:

The index of the input port to linearize around.

<col class="field-name" />
<col class="field-body" />

Returns:	A system implementing the optimal controller in the original
system coordinates.

Raises:	RuntimeError if R is not positive definite. $See also

drake::systems::Linearize()

pydrake.systems.controllers.MakeFiniteHorizonLinearQuadraticRegulator(system: pydrake.systems.framework.System_[float], context: pydrake.systems.framework.Context_[float], t0: float, tf: float, Q: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], R: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], options: pydrake.systems.controllers.FiniteHorizonLinearQuadraticRegulatorOptions = FiniteHorizonLinearQuadraticRegulatorOptions(Qf=None, N=None, input_port_index=InputPortSelection.kUseFirstInputIfItExists, use_square_root_method=False)) → pydrake.systems.framework.System_[float]¶

Variant of FiniteHorizonLinearQuadraticRegulator that returns a System
implementing the regulator (controller) as a System, with a single
"plant_state" input for the estimated plant state, and a single
"control" output for the regulator control output.

See also

FiniteHorizonLinearQuadraticRegulator for details on the
arguments.

class pydrake.systems.controllers.PeriodicBoundaryCondition¶

For algorithms that rely on approximations of the state-dynamics (as
in FittedValueIteration), this is a list of state dimensions for which
the state space maximum value should be "wrapped around" to ensure
that all values are in the range [low, high). The classic example is
for angles that are wrapped around at 2π.

__init__(self: pydrake.systems.controllers.DynamicProgrammingOptions.PeriodicBoundaryCondition, state_index: int, low: float, high: float) → None¶

high¶

low¶

state_index¶

class pydrake.systems.controllers.PidControlledSystem¶

Bases: pydrake.systems.framework.Diagram_[float]

A system that encapsulates a PidController and a controlled System
(a.k.a the "plant").

The passed in plant must meet the following properties:

Input port plant_input_port_index must be all of the control inputs
(size U). When the plant is a dynamics model, this is typically the
generalized effort (e.g., force or torque) command.

The output port passed to the PidControlledSystem constructor must be
of size 2 * Q, where the first Q elements are the position states of
the plant, and the second Q elements are the velocity states of the
plant. Q >= U.

The resulting PidControlledSystem has two input ports with the
following properties:

Input port zero is the feed forward control (size U), which will be added
onto the output of the PID controller. The sum is sent to the plant's
input.

Input port one is the desired controlled states (2 * U) of the plant,
where the first half are the controlled positions, and the second half
are the controlled velocities.

All output ports of the plant are exposed as output ports of the
PidControlledSystem in the same order (and therefore with the same
index) as they appear in the plant.

Some of the constructors include a parameter called
feedback_selector. It is used to select the controlled states
from the plant's state output port. Let S be the gain matrix in
parameter feedback_selector. S must have dimensions of (2 * U,
2 * Q). Typically, S contains one 1 in each row, and zeros
everywhere else. S does not affect the desired state input. Let
'x' be the full state of the plant (size 2 * Q), and 'x_d' be the
desired state (size 2 * U), S is used to compute the state error
as x_err = S * x - x_d.

desired_state→

feedforward_control→

	PidControlledSystem

→ (exported output port of plant, with same name)

→ ...

→ (exported output port of plant, with same name)

__init__(*args, **kwargs)¶

Overloaded function.

__init__(self: pydrake.systems.controllers.PidControlledSystem, plant: pydrake.systems.framework.System_[float], kp: float, ki: float, kd: float, state_output_port_index: int = 0, plant_input_port_index: int = 0) -> None

plant full state is used for feedback control, and all the
dimensions have homogeneous gains specified by Kp, Kd and
Ki.

Parameter plant:

The system to be controlled. This must not be nullptr.

Parameter Kp:

the proportional constant.

Parameter Ki:

the integral constant.

Parameter Kd:

the derivative constant.

Parameter state_output_port_index:

identifies the output port on the plant that contains the (full)
state information.

Parameter plant_input_port_index:

identifies the input port on the plant that takes in the input
(computed as the output of the PID controller).

__init__(self: pydrake.systems.controllers.PidControlledSystem, plant: pydrake.systems.framework.System_[float], kp: numpy.ndarray[numpy.float64[m, 1]], ki: numpy.ndarray[numpy.float64[m, 1]], kd: numpy.ndarray[numpy.float64[m, 1]], state_output_port_index: int = 0, plant_input_port_index: int = 0) -> None

plant full state is used for feedback control, and the vectorized
gains are specified by Kp, Kd and Ki.

Parameter plant:

The system to be controlled. This must not be nullptr.

Parameter Kp:

the proportional vector constant.

Parameter Ki:

the integral vector constant.

Parameter Kd:

the derivative vector constant.

Parameter state_output_port_index:

identifies the output port on the plant that contains the (full)
state information.

Parameter plant_input_port_index:

identifies the input port on the plant that takes in the input
(computed as the output of the PID controller).

__init__(self: pydrake.systems.controllers.PidControlledSystem, plant: pydrake.systems.framework.System_[float], feedback_selector: numpy.ndarray[numpy.float64[m, n]], kp: float, ki: float, kd: float, state_output_port_index: int = 0, plant_input_port_index: int = 0) -> None

A constructor where the gains are scalar values and some of the
plant's output is part of the feedback signal as specified by
feedback_selector.

Parameter plant:

The system to be controlled. This must not be nullptr.

Parameter feedback_selector:

The matrix that selects which part of the plant's full state is
fed back to the PID controller. For semantic details of this
parameter, see this class's description.

Parameter Kp:

the proportional constant.

Parameter Ki:

the integral constant.

Parameter Kd:

the derivative constant.

Parameter state_output_port_index:

identifies the output port on the plant that contains the (full)
state information.

Parameter plant_input_port_index:

identifies the input port on the plant that takes in the input
(computed as the output of the PID controller).

__init__(self: pydrake.systems.controllers.PidControlledSystem, plant: pydrake.systems.framework.System_[float], feedback_selector: numpy.ndarray[numpy.float64[m, n]], kp: numpy.ndarray[numpy.float64[m, 1]], ki: numpy.ndarray[numpy.float64[m, 1]], kd: numpy.ndarray[numpy.float64[m, 1]], state_output_port_index: int = 0, plant_input_port_index: int = 0) -> None

A constructor where the gains are vector values and some of the
plant's output is part of the feedback signal as specified by
feedback_selector.

Parameter plant:

The system to be controlled. This must not be nullptr.

Parameter feedback_selector:

The matrix that selects which part of the plant's full state is
fed back to the PID controller. For semantic details of this
parameter, see this class's description.

Parameter Kp:

the proportional vector constant.

Parameter Ki:

the integral vector constant.

Parameter Kd:

the derivative vector constant.

Parameter state_output_port_index:

identifies the output port on the plant that contains the (full)
state information.

Parameter plant_input_port_index:

identifies the input port on the plant that takes in the input
(computed as the output of the PID controller).

get_control_input_port(self: pydrake.systems.controllers.PidControlledSystem) → pydrake.systems.framework.InputPort_[float]¶

<col class="field-name" />
<col class="field-body" />

Returns:	the input port for the feed forward control input.

get_state_input_port(self: pydrake.systems.controllers.PidControlledSystem) → pydrake.systems.framework.InputPort_[float]¶

<col class="field-name" />
<col class="field-body" />

Returns:	the input port for the desired position/velocity state.

get_state_output_port(self: pydrake.systems.controllers.PidControlledSystem) → pydrake.systems.framework.OutputPort_[float]¶

class pydrake.systems.controllers.PidController¶

Bases: pydrake.systems.framework.LeafSystem_[float]

Implements the PID controller. Given estimated state x_in = (q_in,
v_in), the controlled state x_c = (q_c, v_c) is computed by
x_c = P_x * x_in, where P_x is a state projection matrix. The
desired state x_d = (q_d, v_d), is in the same space as x_c.
The output of this controller is:

y = P_y * (kp * (q_d - q_c) + kd * (v_d - v_c) + ki * integral(q_d - q_c)),

where P_y is the output projection matrix.

estimated_state→

desired_state→

	PidController

→ control

This system has one continuous state, which is the integral of
position error, two input ports: estimated state x_in and desired
state x_d, and one output port y. Note that this class assumes
|q_c| = |v_c| and |q_d| = |v_d|. However, |q_c| does not
have to equal to |q_d|. One typical use case for non-identity
P_x and P_y is to select a subset of state for feedback.

__init__(*args, **kwargs)¶

Overloaded function.

__init__(self: pydrake.systems.controllers.PidController, kp: numpy.ndarray[numpy.float64[m, 1]], ki: numpy.ndarray[numpy.float64[m, 1]], kd: numpy.ndarray[numpy.float64[m, 1]]) -> None

Constructs a PID controller. P_x and P_y are identity matrices
of proper sizes. The estimated and desired state inputs are 2 *
kp's size, and the control output has kp's size.

Parameter kp:

P gain.

Parameter ki:

I gain.

Parameter kd:

D gain.

<col class="field-name" />
<col class="field-body" />

Raises:

RuntimeError if kp, ki and kd have different

dimensions.

__init__(self: pydrake.systems.controllers.PidController, state_projection: numpy.ndarray[numpy.float64[m, n]], kp: numpy.ndarray[numpy.float64[m, 1]], ki: numpy.ndarray[numpy.float64[m, 1]], kd: numpy.ndarray[numpy.float64[m, 1]]) -> None

Constructs a PID controller. Calls the full constructor, with the
output projection matrix P_y being the identity matrix.

Parameter state_projection:

The state projection matrix P_x.

Parameter kp:

P gain.

Parameter ki:

I gain.

Parameter kd:

D gain.

<col class="field-name" />
<col class="field-body" />

Raises:

RuntimeError if kp, ki and kd have different

dimensions or `P_x.row() != 2 * |kp|'.

__init__(self: pydrake.systems.controllers.PidController, state_projection: numpy.ndarray[numpy.float64[m, n]], output_projection: numpy.ndarray[numpy.float64[m, n]], kp: numpy.ndarray[numpy.float64[m, 1]], ki: numpy.ndarray[numpy.float64[m, 1]], kd: numpy.ndarray[numpy.float64[m, 1]]) -> None

Constructs a PID controller. This assumes that

1. |kp| = |kd| = |ki| = |q_d| = |v_d|
  2. 2 * |q_d| = P_x.rows
  3. |x_in| = P_x.cols
  4. |y| = P_y.rows
  4. |q_d| = P_y.cols

Parameter state_projection:

The state projection matrix P_x.

Parameter output_projection:

The output projection matrix P_y.

Parameter kp:

P gain.

Parameter ki:

I gain.

Parameter kd:

V gain.

<col class="field-name" />
<col class="field-body" />

Raises:	RuntimeError if any assumption is violated.

get_input_port_desired_state(self: pydrake.systems.controllers.PidController) → pydrake.systems.framework.InputPort_[float]¶

Returns the input port for the desired state.

get_input_port_estimated_state(self: pydrake.systems.controllers.PidController) → pydrake.systems.framework.InputPort_[float]¶

Returns the input port for the estimated state.

get_Kd_vector(self: pydrake.systems.controllers.PidController) → numpy.ndarray[numpy.float64[m, 1]]¶

Returns the derivative gain vector.

get_Ki_vector(self: pydrake.systems.controllers.PidController) → numpy.ndarray[numpy.float64[m, 1]]¶

Returns the integral gain vector.

get_Kp_vector(self: pydrake.systems.controllers.PidController) → numpy.ndarray[numpy.float64[m, 1]]¶

Returns the proportional gain vector.

get_output_port_control(self: pydrake.systems.controllers.PidController) → pydrake.systems.framework.OutputPort_[float]¶

Returns the output port for computed control.

        Next

         Previous

          C++

          Python

          GitHub

redpajama_set_name: RedPajamaGithub


Our target should be to consolidate and improve the high-quality and repair of current goods, in the meantime regularly produce new solutions to meet unique customers' needs for Teks Self Tapping Screws , teks self tapping screws , self tapping screws , Our tenet is evident all of the time: to deliver high quality solution at competitive price tag to clients throughout the planet. We welcome potential customers to get in touch with us for OEM and ODM orders.
"We're commitment to offer the competitive rate ,exceptional products and solutions high quality, too as fast delivery for Teks Self Tapping Screws , teks self tapping screws , self tapping screws , What is good price? We give customers with factory price. In the premise of good quality efficiency must be paid attention to and maintain appropriate low and healthy profits. What is a fast delivery? We make the delivery according to customers' requirements. Although delivery time depends on the order quantity and the complexity of it we still try to supply solutions in time. Sincerely hope we could have long term business relationship.


text:
Accueil > Books>Death of Louis XIV
Death of Louis XIV
This day was the only one whose mastery has escaped the Great King, he who wanted the almighty officer of his kingdom. Examine the scope of the death of Louis XIV led to reconsider this very long reign in terms of the political project that the prince himself had designed. This book gives to understand what goes out with the Sun King and who continues his work. What is the singular greatness of the age of Louis XIV? The glory, the king of war, the "state machine", the factory of royal culture: that sovereign elevated the prestige of the French monarchy at the peak of its influence; he completed installing the administrative apparatus of the old regime by including it in the gene pool of our institutions; he erected the "state secrets" method of government and merges the glory of his sacred figure even in the humblest cottage. It was an inordinate ambition that the tests will eventually disrupt. What a contrast between the young monarch, ardent reformer in the "Colbert years," which leaves its mark to all forms of creation in the excitement of a Versailles Baroque and festive, and the old king proven by endless wars in the Prancing devotion chasing the enemies of the faith! The death of Louis XIV closes a chapter in the history of royalty and opens another: at the dawn of the Enlightenment, it is the "how" of this monarch is also a certain conception of authority which died with him.
Author : Joel Cornette
Editor : Gallimard
Date of release : 07/08/2015

redpajama_set_name: RedPajamaCommonCrawl


In the REIMEP-18 campaign laboratories were invited to measure uranium isotopic ratios in nitric acid. Each participating laboratory was provided with four samples each containing 2.5 mg of depleted to slightly enriched uranium (235U abundance between ca. 0.2 % and 4.5 %) in 0.5 mL of 0.5 M nitric acid.
m(234U)/m(U), m (235U)/m(U), m(236U)/m(U), m (238U)/m(U).
IRMM supplied the samples blind, i.e. without certified isotopic abundance values.
On receipt of the measured values IRMM sent the certified values to the participant.
IRMM published a participants' report showing the results relative to the certified values in a graphical form.
The links between results and identity of the participating laboratory are not published.
The total nuclear activity of the four REIMEP-18 samples is less than 1000 Bq so materials were shipped using DHL or a similar carrier. The material was not declared as radioactive and therefore no license declarations were required from participants.
IRMM charged a fee of € 200 for administrative and transport costs. This fee was waived for specific laboratories, in particular those from the new Member States and the Acceding Countries to the EU: please inquire directly.
If you have questions about REIMEP-18, please contact Stephan Richter, the campaign coordinator (E-mail jrc-irmm-reimep@ec.europa.eu).
Registration for participation in the campaign was performed on-line.
The registration forms were available on-line until 28 February 2006. A signed copy of the registration form was to be faxed to Stephan Richter (fax: +32-(0)14 571 863), REIMEP-18 co-ordinator by the end of February 2006.
Important: Registration was only definitive when the copy of the signed registration form was received by IRMM.
an instruction letter containing the allocated sample codes and password to be used for the on-line results reporting.
The measurement results were to be reported via the IRMM web database system. The result reporting pages were accessible from this site. To open the reporting pages the password allocated to each participant had to be used when logging into the system. This password is unique to the participant and campaign.
but reports with partial results i.e. only some of these ratios were also accepted.
The result reporting forms had to be submitted by the end of May 2006.


text:
CNN leaving CNN Center building in downtown Atlanta
ATLANTA (AP) — CNN is moving out of the CNN Center, its longtime downtown Atlanta home by the end of this year.
The cable channel's weekday anchors are all already in New York or Washington, but CNN still has digital and CNN International operations in Atlanta. Spokesperson Bridget Leininger confirmed in an email that the remaining CNN staff and operations in Atlanta would move to the Techwood Turner Broadcasting campus in Midtown.
The move will happen in stages and will finish by the end of this year, Leininger said.
CNN's previous parent company, AT&T, sold the CNN Center for nearly $164 million to two Florida-based real estate firms, CP Group and Rialto Capital, in 2021, The Atlanta Journal-Constitution reported. It was not immediately clear what would happen to the building's other tenants.
WVU researcher looks to improve shale gas conversion …
West Virginia Italian Heritage Festival hosts wine …
Can you identify this woman? Bridgeport Police Department …
West Virginia has lowest racial/ethnic wealth gap …
Starbucks fans are steamed: The psychology behind …
Where the heck is 'Flipping,' West Virginia? and …
West Virginia man arrested for allegedly abusing, …


Most things are reportedly still there, and a new farm-themed topic has been added, to introduce kids to NC livestock and crops. I'm glad to see that the new train table is actually bigger, I was a bit worried it would have to make place for something else. ("Don't mess with Thomess!") I think we were actually there the last day that it was open, and it would only be appropriate to go back on the first day it re-opens.
This entry was posted in Action, Active, Animals, Crafts, Food, Indoors, Other, Raleigh, Science, Trains by daddyweekly. Bookmark the permalink.


text:
from __future__ import unicode_literals

from django.conf.urls import url,include
from rest_framework.routers import SimpleRouter
from viewsets import CategoryViewSet

from . import views

router = SimpleRouter(trailing_slash = True)
router.register(r'rest',CategoryViewSet)

urlpatterns = [
    url(r'^$', views.IndexView.as_view(), name='index'),

    url(r'^(?P<pk>\d+)/$', views.detail, kwargs={'slug': "", }, name='detail'),
    url(r'^(?P<pk>\d+)/(?P<slug>[\w-]+)/$', views.detail, name='detail'),
    url(r'',include(router.urls)),
]


text:
Troubled Faraday Future will build a factory in China in 2025
Basith Rahman
Remember the beleaguered Faraday Future? The EV company appears not ready to die out just yet as it has announced plans to build a factory in China by 2025. Faraday disclosed this during an investor briefing.
However, before this announcement, Faraday Future had revealed in a filing with the US Securities Exchange Commission (SEC) that it had plans new factory in China.
With this news, there have been questions about whether former CEO Jia Yueting would return to the company he co-founded. Yueting has been involved in multiple financial controversies in connection with the many companies he either founded or led as CEO. He filed for bankruptcy in 2019 with over US$3.6 billion in personal debt.
Meanwhile, Faraday Future remains mired in financial trouble, as shown by its Q1 2022 financial report. The company's operating loss was about US$149 million, significantly more than the $19 million it lost in the same period in 2021. Net loss stood at $153 million, more than double of Q1 2021. Last year's full-year net loss was US$517 million, more than three times its total loss in 2020.
However, Faraday Future said at the time that the increase in net loss was due to a rise in operating expenses, which resulted from more investments in engineering, design, and testing (ED&T) services as it gears up to start manufacturing the FF 91. Part of the expenses was paying Geely Holdings for using its technology platform. Geely was announced last year as the manufacturing partner for Faraday Future in China. The company also spent significantly on legal services.
Faraday Future insists the FF 91 will enter production in the third quarter of this year, which would be a culmination of five years of intrigue since the crossover EV was revealed in 2017. The company released a 'production intent' prototype of the FF 91 earlier this year, built at its Hanford, California plant. However, going by its history of missing self-enforced deadlines, we can only wait and see if any car would roll off Faraday Future's assembling line.
You can read more about the tumultuous history of Faraday Future here by my colleague Leo.
Sources: Zaker, My Drivers, Sina Finance


These Books are all based on Lottie's little boy William…. they are stories that capture the imagination of little ones and are full of wonderful adventure and dreams… or are they dreams?? In this first story, William falls asleep and dreams that he is a tiger. When he wakes up he begins to realise that it might not have been a dream after all…..
Designed to help with language development and to teach children about animals in a fun and imaginative way, this is a must read for all children and parents to aid peaceful sleep.
This year Night Night Little Tiger is to also be featured on CBeebies Bedtime Stories. Be Sure to look out for it!
The author Lottie Prentice is a successful children's author passionate about children's literature and education. She believes that children are never too young to develop a strong understanding of language and all too often their capacity to understand and thirst for knowledge are underestimated.
DOM JOLY – Comedian & Journalist.
JODIE KIDD – Model & TV Personality.
JERRY HIBBERT – Award winning Producer, Director and Animator.
TWEEDY – The Legendary Clown.
Lottie has also been getting out there with the promotion!


Trying to teach people to trust God's discipline and correction without first demonstrating and giving them an appreciation for His love is like expecting someone to pet a growling, barking dog just because you told them it was friendly.
No one is going to accept discipline, being told certain actions are wrong, when they have no comprehension of the love reasoning behind it.
It is the same way with children. Without a foundation of love and trust, they will automatically assume you are trying to limit them when you tell them "no" rather than to protect them out of love. And with their lack of experience-gained wisdom that you have, there is no way they can truly understand your reasoning; it has to come from trust/faith, just as following God's restrictions come from trust that He had a perfect reason for His guidelines, and it is all for the greater good.